How fast and robust is the quantum adiabatic passage?

Abstract

We study the assisted adiabatic passage, and equivalently the transitionless quantum driving, as a quantum brachistochrone trajectory. The optimal Hamiltonian for given constraints is constructed from the quantum brachistochrone equation. We discuss how the adiabatic passage is realized as the solution of the equation. The formulation of the quantum brachistochrone is based on the principle of least action. We utilize it to discuss the stability of the adiabatic passage.

16 pages, 4 figures; minor changes for v2

References in corpus (11)

• Shortcut to adiabatic passage in two and three level atoms
• Lewis-Riesenfeld invariants and transitionless tracking algorithm
• Optimally robust shortcuts to population inversion in two-level quantum systems
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Robust quantum control by shaped pulse
• Experimental implementation of assisted quantum adiabatic passage in a single spin
• Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
• Transitionless quantum driving for spin systems
• Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors
• Fast and robust spin manipulation in a quantum dot by electric fields
• Dynamical invariants for quantum control of four-level systems

Cited by in corpus (23)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
• Hamiltonian engineering via invariants and dynamical algebra
• Focus on Shortcuts to Adiabaticity
• Shortcuts to adiabaticity for quantum annealing
• Shortcuts to adiabatic passage for fast generation of Greenberger-Horne-Zeilinger states by transitionless quantum driving
• Probing Quantum Speed Limits with Ultracold Gases
• Nonadiabatic Control of Geometric Pumping
• From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
• Fast-forward scaling in a finite-dimensional Hilbert space
• Hamiltonian engineering for adiabatic quantum computation: Lessons from shortcuts to adiabaticity
• Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
• Shortcuts to adiabaticity in non-Hermitian quantum systems without rotating-wave approximation
• Unitary deformations of counterdiabatic driving
• Shortcuts to adiabaticity applied to nonequilibrium entropy production: An information geometry viewpoint
• Optimization of Markov process violates detailed balance condition
• Nonadiabatic energy fluctuations of scale-invariant quantum systems in a time-dependent trap
• Counterdiabatic Formalism of Shortcuts to Adiabaticity
• Transition probability generating function of a transitionless quantum parametric oscillator
• Quantum acceleration by an ancillary system in non-Markovian environments
• Dynamical invariant formalism of shortcuts to adiabaticity
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra